Progress In Electromagnetics Research, PIER 69, 47–54, 2007
MEASUREMENT OF DIELECTRIC CONSTANT AND
LOSS FACTOR OF THE DIELECTRIC MATERIAL AT
A. Kumar and S. Sharma
Department of Electronics and Communication Engineering
S. D. D. Institute of Engineering and Technology
Department of Electronics and Communication Engineering
Jaypee University of Information Technology
Solan, 173 215, India
Abstract—A new technique to evaluate the dielectric constant and
loss factor of a homogeneous dielectric material using rectangular
shaped perturb cavity has been developed. The values of S-parameters
are measured experimentally by placing the sample in the center of
the cavity resonator. Sample under test is fabricated in the form of a
cylinder. The real and imaginary part of the permittivity can be then
calculated from the shift in the resonance frequency and Q-factor. The
results of a Teflon sample are also tabulated.
The dielectric constant is an essential property of dielectric materials
hence its determination is very important. There are many techniques
have been developed to this end [1–14].
depends on the measurement of either reflection coefficients or resonant
frequencies.In the later case material is characterized to load a
resonant cavity [2–11] and the sample permittivity is evaluated from
the shift of the resonant frequency value, compared to that of the
empty (unload) cavity. This approach is based on the perturbation
theory, thus it requires the sample to be small enough so that field
distribution inside the empty cavity changes slightly when the cavity
is loaded. The cavity perturbation method for the measurement of
The most used technique
48 Kumar, Sharma, and Singh
dielectric constant is different from other methods and very sensitive.
It involve approximations in their formulation which lead to acceptable
results only under very restricted conditions: (i) The sample must
be very small compared with the cavity itself so that a frequency
shift which is small compared with the resonant frequency shift of
the empty cavity is produced by the insertion of the sample. (ii) The
cavity without and with sample must be very much alike. The cavity
perturbation method has been extensively used for measuring dielectric
parameters of material at microwave frequencies. This measurement
method can be highly accurate and particularly advantageous in the
determination of small loss tangent or loss factors.
This paper introduces new cavity perturbation technique in which
a cavity has been designed with very small slot at the center of
broader side of the waveguide in order to insert a sample material.
Using cavity perturbation technique rectangular cavity resonator is
designed to measure the dielectric parameters of Teflon. Measuring
resonance frequency of empty cavity and then measuring the shift in
resonance frequency with the sample material placed at its center and
then the dielectric constant is calculated from the shift in resonance
frequency and the sample volume whereas the loss factor is calculated
from quality factor with and without sample.
test (Teflon) is fabricated in the form of a cylinder and inserted into
the center of the rectangular cavity. This measurement method also
describes the application of perturbation method to a microwave cavity
resonator with a dielectric perturber. The measurement setup uses
rectangular waveguide cavity resonator, HP8510 Network Analyzer
and PC. The real and imaginary part of the permittivity can then
be calculated from the shift in the resonance frequency and Q-factor.
The result shows that the dielectric constant of the material can be
measured with existing cavity with good accuracy.
The material under
2. THEORETICAL ANALYSIS
Many researchers have reported the theoretical [12–14] and experimen-
tal [2–11] results of the cavity perturbation techniques. The measure-
ments of permittivity and permeability of the dielectric materials are
performed by inserting a small and appropriately shaped sample into
a cavity and determining the properties of the sample from the resul-
tant change in the resonant frequency and loaded quality factor of the
cavity. The basic idea of the cavity perturbation is the change in the
overall geometric configuration of the electromagnetic fields with the
insertion of a small sample must be small. Based on this assumption, a
detailed derivation of the perturbation equation for the frequency shift
Progress In Electromagnetics Research, PIER 69, 2007 49
upon the insertion of a sample into a cavity was given by Harrington
. When a small sample is inserted in a cavity which has an electric
field E0and magnetic field H0in the unperturbed state and the fields
in the interior of the sample is E and H, then for loss less sample, the
variation of resonance frequency is given by [1,6] as
(∆εE · E∗
0+ ∆µH · H∗
0+ µH · H∗
(εE · E∗
where ε and µ are the permittivity and permeability of the medium
in the unperturbed cavity.
dτ is the elementary volume and ∆ε
and ∆µ are the changes in the permittivity and permeability due to
the introduction of the sample in the cavity. Without affecting the
generality of Maxwell’s equations, the complex frequency shift due to
lossy sample in the cavity is given by [2,3,6] as
E · E∗
0dv + (µr− 1)µ0
H · H∗
where df∗is the complex frequency shift because the permittivity of
practical materials is a complex quantity, so the resonance frequency
is also complex. B0,H0,D0and E0are the fields in the unperturbed
cavity and E and H is the field in the interior of the sample [4,12].
In terms of energy, the numerator of equation (2) represents the
energy stored in the sample and the denominator represents the total
energy stored in the cavity. The total energy W = We+ Wmwhere
Weand Wmare the electric and magnetic energy, respectively. With
the aforementioned assumptions applied on equation (2), the fields in
the empty part of the cavity are negligible changed by the insertion
of the sample. The fields in the sample are uniform over its volume.
Both of these assumptions can be considered valid if the sample is
sufficiently small relative to the resonant wavelength. The negative
sign in equation (2) indicates that by introducing the sample, the
resonance frequency is lowered. When a dielectric sample is inserted
into the cavity resonator where the maximum perturbation occurs that
is at the position of maximum electric field, only the first term in the
numerator is significant, since a small change in εrat a point of zero
electric field or a small change in µrat a point of zero magnetic field
does not change the resonance frequency. Therefore equation (2) can
50 Kumar, Sharma, and Singh
be reduced to
E · E∗
3. DIELECTRIC CONSTANT ε?AND LOSS FACTOR ε??
A sample of complex permittivity εr = ε?− jε??is kept at the
maximum electric field location of the cavity. The sample is taken,
as cylinder with uniform cross sectional area ‘s’ and length is greater
than narrow dimension ‘b’ so that it will occupy the entire narrow
dimension of the cavity. After the introduction of the sample the
empty resonant frequency and Q-factor alter, due to the change in the
overall capacitance and conductance of the cavity. If f0and Q0are the
resonance frequency and quality factor of the cavity without sample
and fsand Qsall the corresponding parameters of the cavity loaded
with the sample. The complex resonant frequency shift is related to
measurable quantities by [2,6,12]
On equating real and imaginary parts of equation (3) and (4) we have
For real part:
E · E∗
We may assume that E = E0and the valve of E0in the TE10pmode
is E0= E0maxsin(pπz/l)sin(pπz/l) where a is the broader dimension
of the wave guide and l is the length of the cavity. Integrating and
rearranging the equation (5), we obtain
where Vcis volume of the cavity = a×b×l (Dimensions of the cavity)
and Vsis the volume of the sample = πr2h (r is the radius and h is
the length of the sample).
Progress In Electromagnetics Research, PIER 69, 2007 51
For Imaginary part:
E · E∗
Integrating and rearranging the equation (7), we obtain
where Qs is the quality factor of cavity with sample and Q0 is the
quality factor without sample. Equation (6) and (8) are the standard
form of the expression for dielectric parameters using the perturbation
4. EXPERIMENTAL SET UP
A rectangular X band waveguide cavity is constructed with a brass
waveguide of nearly 140mm length.
are 22.9mm in width and 10mm in height.
sheets are used to form the cavity and to close the two ends of the
waveguide. The inductive coupling is provided with two symmetric
holes of diameter 4mm on these end sheets. Fig. 1 and Fig. 2 show
the cavity resonator and block diagram of experimental setup for the
In order to insert a sample material into the resonator, a slot is
constructed at the center of the broader side of the waveguide. The
The cross section dimensions
Two thin conducting
Coupling hole 4mm
Figure 1. The cavity resonator and its dimensions.
52 Kumar, Sharma, and Singh
S - PARAMETER
TEST SET UP
ANALYSER HP 8510
Figure 2. Block diagram of the experimental setup.
Figure 3. Transmission coefficients of the Cavity measurements in
Table 1. Dielectric constant of Teflon.
ε ε ε ε′ ′ ′ ′
Progress In Electromagnetics Research, PIER 69, 2007 53
width of the sample hole is equal to the diameter of the cylindrical
sample. This rectangular waveguide cavity resonator is connected to
the two ports of the HP 8510 s-parameter test set of the measuring
system. It is also operated in the TE10P modes.
5. EXPERIMENTAL RESULTS
An example of the cavity measurement in X-band is shown in Fig. 3.
The left peaks of the Fig. 3 are the resonance peaks of the cavity
containing sample (Teflon) material and the right peaks are the
empty cavity resonance. Fig. 3 shows the expected shift in resonance
frequency and Q-factor. The obtained resonance parameters and
dielectric calculation are tabulated for TE105 mode. Table 1 shows
the calculated values of dielectric constant of cylindrical Teflon sample
of different radius.
A new perturbation technique has been developed and discussed for the
evaluation of dielectric parameters of dielectric material at microwave
frequency. In this technique, a cavity has been designed with very small
slot at the center of the broader side of the wave-guide in order to insert
a sample material. The existing cavity resonator is constructed with
a line slot on the broader side of the wave-guide with moving sample
holder. The analysis of the expressions for dielectric constant and loss
factor has been discussed. It has been observed from the results that
the dielectric parameters of the material can be measured with existing
cavity with good accuracy.
The authors are sincerely thankful to reviewers for their critical
comments and suggestions to improve the quality of the manuscript.
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